Arcofactor.



PATENTED OCT. 25, 1904.

A. P. STOKES.

AROOPAGTOR. I APPLIQATIONIILED 0017. 1903.

2 SHEETSSHEBT 1.

N0 MODEL.

Anson Phegps Szolcesjn Veniar,

by/r-r, 6217, M Aizs Witnesses:

No. 773,299. PATENTED OUT. 25, 1904. A. P. STOKES. ARGOPAUTOR.

APPLIOATION FILED OUT. 7. 1903. N0 MODEL. ZSHEETS-SHEET 2.

Fig.2

Wiinesses: v Anson Phelps Szokes, 11211622502 lay/ W4 1, W AZ Z QSPatented October 25, 1904.

PATENT OFFICE.

ANSON PHELPS STOKES, OF NEW YORK, N. Y.

ARCOFACTOR- SPECIFICATION forming part of Letters Patent N0. 773,299,dated October 25, 1904..

Application filed October 7, 1903.

T0 (LZZ whom, it may concern.-

Be it known that I, Anson PHELPS S'roKEs, a citizen of the UnitedStates, residing at New York, in the county and State of New York, haveinvented certain new and useful Improvements in Arcofactors, of whichthe following is a specification, reference being had to the drawingsaccompanying and forming part of the same.

My invention relates to instruments for describing arcs of circles andother curves without reference to the actual center or foci, andtherefore provides a means for readily drawing arcs of long radii. Wherethe radius is not more than about two or three feet, an ordinarybeam-compass can generally be used; but where the radius is much longer,up to several hundred feet, it becomes practically impossible to drawthe are by continuous motion with a device which is pivoted at theactual center of curvature.

In my device I make use of the geometrical principle that all angles atthe circumference of a circle subtended by the same chord are equal.Assuming arbitrarily a line of any convenient length as the chord of thearc to be described, if at the center of this line a perpendicular beerected equal in length to the versed sine of one-half the arc theextremity of the perpendicular will be at the middle of the arc. Then byconnecting this extremity with the ends of the chord an isoscelestriangle will be formed whose vertical angle is the constant subtendedangle of the chord. If now an infinite number of triangles with equalvertical angles be drawn on the chord as a base, the locus of the apexesof the triangles will be the are desired. This latter might be drawntentatively by erecting a greater or less number of triangles, accordingto the degree of approximation to geometrical exactness desired; but thepreferred method is to describe the locus by the continuous 'motion of apoint. Various devices for effecting. this have been proposed,consisting in one form or another of a pair of pivoted armscorresponding to the sides of the constant angle. By clamping the armsrigidly in adjusted position and moving them so that they are .always incontact each with Serial No. 176,038- (No model.)

itsrespective end of the chord the apex will describe the desired arc,as will be readily understood. My present invention, which forms thesubject of this application, likewise embodies this idea, but providesfor a number of novel features and combinations and has advantages ineffectiveness and range and in simplicity, consisting, as it does, ofthree pieces of wood or of other suitable materials pivoted together, apivoted tongue, and a device for clamping the parts in adjusted positionhaving also an attachment to hold a pencil or other marker. Thesefeatures will be easily understood when described in connection with theaccompanying drawings, in which Figure 1 is a diagram illustrating thegeometrical and trigonometrical principles of the device; Fig. 2, a planview of the instrument arranged for use; Fig. 3, a detail view of partofthe same; Fig. 4.. a diagram-showing amethod of repeating the arc, andFig. 5 is a side view of a convenient device for securing the arms ofthe instrument in adjusted position.

In Fig. l the line A B is the arbitrarilyassumed chord. C D is theversed sine of onehalf the arc to be drawn. Then A C B is the inscribedtriangle. sides A C and B C be moved bodily, always maintaining the sameangle between them and keeping them or their lineal extensions alwaystouching the extremities of the chord,as shown in the fulland dottedlines of the figure, the point C will traverse the desired arc. Thepreferred embodiment of my invention, which utilizes these principles,is shown in Fig. 2. The instrument consists of a base or bar D of anyconvenient size, according to the radii of the arcs to be described. Forradii from thirty inches to seventy-five feet or more a length of fivefeet three and one-half inches will be suitable. Pivoted at each end ofthis, as shown, are arms E F, the three being so constructed that thecenters of the pivots are exactly at the verticesof the angles formed bythe inner edges of the base D and arms E F. It is now evident that thearms may be swung upward or downward to form Within obvious limits anyangle between them. Piv- It is obvious that if the 1 oted at aconvenient point in a transverse line bisecting the base D is a tongue(1?, preferably about fifteen inches in length for a base of the sizementioned above. This tongue, which for COHVOIllOI'lCO may be made oftransparent material. has a number of perforations therein. In using theinstrument one of these perforations will be placed at the point atwhich the inner edges of the arms cross, and conse quently at the vertexof the constant angle. For securing the movable parts in adjustedposition any convenient device may be employedas, for example, a clamp,as H, which may have an extension 1, with an aperture in the latter inwhich a pencil may be inserted.

The operation of the instrument will be readily understood from thefollowing. In Fig. 2, J represents the surface on which an arc is to bedrawn as, for example, a drawil'igboardon which is tacked a sheet ofpaper K. On the sheet draw two straight lines, crossing at right anglesat L. Below the horizontal line and touching it place two stout pins A Bon opposite sides of L and each fifteen inches therefrom.- This part ofthe horizontal line represents the chord of the are to be drawn. Thenone-half this chord, lifteen inches, is the sine of one-half the are tothe given radius R, and the extremity of the versed sine of one-half ofthe same, laid off on the perpendicular, will mark the highest point ofthe whole are. To determine the value of the versed sine, the formulaversin I R E1i may be used. the formula becomes versin R F i5 and thevalue of R. the radius, having been inserted the value of the versedsine is readily found. Having determined the extremity of the versedsine, as at C, place the base of the arcofactor below the horizontalline, as follows: Central pivot on perpendicular line. Inner edges ofarms touching the pins, so that the junction of the inner sides of armsand one of the holes in the transparent tongue shall be over the upperextremity of the versed sine. Clamp arms and tongue in this position bymeans of the clamp. Insert the sharp point of a marker in this hole andswing the arcofactor as far as the pins will permit, keeping the inneredges of the arms constantly touching the pins, and the required arewill be drawn to within a short distance of each end. On a sheet ofsufiicient size the first are may be completed and extended in thefollowing manner, as illustrated in Fig. 4:. \Vith one end of horizontalline as a center and with a radius equal to the versed sine describe Thesine being fifteen inches,

This will give a new chord base-line of thirty inches by which a secondarc of the required radius may be described with the arcofactor andforming a continuation of the first are. The curve may be extendedfarther in the same direction by describing a second small are, U, withthe point C as a center and drawing the line A B" tangent thereto andthirty inches in length, as before, for a new base-line. This proceduremay be carried out on either side of the first are as often as permittedby the size of the drawing-surface. If it is desired to draw a number oftrial arcs, as in preliminary work of ship or yacht designing, layingout railways, &c., it will be found convenient to have the horizontaland perpendicular lines in ink and with ink-markings for inches andfractions thereof on the latter up and down from the point ofintersection.

The perforations in the transparenttongue G (shown in detail in Fig. 3)are of course all located in line with its pivot, and since navalarchitects and civil engineers in this country usually employ a scale inwhich one-eighth of an inch or a multiple thereof, as three-eighths, isthe unit length the perforations are placed one-eighth of an inch apart,beginning, say, one inch from the pivot. If new a second series ofperforations one-eighth of an inch apart be located alongside the first,but beginning one and one thirty-second of an inch from the center ofthe pivot, the difference in distance from the center of the pivot Mbetween corresponding openings in the two rows will be one thirty-secondof an inch on the principle of the well-known diagonal scale. lVhen thearms of the areofactor are crossed at the next higher perforation in theadjoining row of perforations, however, the arms will no longer touchthe pins, and the instrument must therefore be moved downward until theyare in contact. The increment actually added to the versed sine willtherefore not be one thirty-second, but one sixty-fourth instead. InFig. 3 l have shown a tongue with four radial rows of perforations,beginning, respectively, one, one and one thirty'second, one andone-sixteenth,and one and three thirtyseconds inches from the pivot. Inusing an instrument with the holes so located the following simple rulesmay be followed: 1f the versed sine be a multiple of one-sixteenth of aninch, use a hole in the left-hand row; if one sixtyfourth more than amultiple of one-sixteenth of an inch, use the next row; if onethirty-second more than a multiple of one sixteenth of an inch, use thethird row; if three sixty-fourths more than a multiple of onesixteenthof an inch, use the fourth row. 1f the arc is given and it is desired tofind the radius, the problem may be readily solved by means of thearcofactor. Draw a chord thirty inches in length, and placing theinstrument over the same as if to draw an arc arrange the arms so thatthey intersect at the extremity of the versed sine. Then adjust thetrans parent tongue so that one of its perforations coincides with thepoint of intersection, and the length of the versed sine can be readdirectly from the tongue. By the formula Yglll the value of R will be 2versin 2 found in inches, or by referring to a table giving radii forversed sines of from one sixty-fourth of an inch to four inches, Withaconstant sine of fifteen inches, the radius may be found directly. Sucha table may be printed or pasted on the instrument itself.

Having now described my invention and in what manner the same may beused, What 1 claim as new, and desire to secure by Letters Patent, is

1. In an instrument for describing arcs, the

combination of a rigid, rectilinear base, an

arm pivoted at each end of the base and adapted to cross at the side ofthe base, a tongue pivoted to the base midway between the arms, having arow of equidistant perforations radiating from the pivot, and one ormore similar rows, each beginning on an are passing between adjacentperforations in the next preceding roW, as set forth.

ANSON PHELPS STOKES. Witnesses:

S. S. DUNHAM, J. R. JoHNsoN.

